Acting on a tip, police raided a house in the central Sulawesi town of Poso town early on Thursday where nine alleged Muslim fighters were staying, police said.
The men reportedly hurled at least eight bombs at police and opened fire with automatic weapons.
Officers returned fire, killing two of them, while seven were arrested.
No other details were given of the police officer reportedly killed at the subsequent funeral.
State news agency Antara quoted police naming one of the dead men as Riyan, alias Abdul Hakim, a senior member of Jemaah Islamiyah who had trained at an al-Qaeda camp in Afghanistan before the US-led invasion in 2001.
Jemaah Islamiyah members have been blamed for a string of bombings in Indonesia since 2000, the most deadly being the 2002 Bali nightclub attacks that killed 202 people, most of them foreign tourists.
Police said they seized bombs, automatic weapons, other makeshift weapons and several handguns and grenade launchers from the house in Poso.
Christian-Muslim violence
Central Sulawesi has been tense since the execution of the three Christian fighters over their role in the sectarian clashes between Muslim and Christian mobs that gripped the region from 1998 to 2001.
In October, an armed group clashed with police and set fire to a Christian church in Poso, while a priest was shot in Palu, sparking fears of a resurgence in sectarian violence.
Three years of clashes in Central Sulawesi killed more than 2,000 people before a peace accord took effect in late 2001.
There has been sporadic violence ever since. Security officials have said that several Jemaah Islamiyah members were hiding out in the area and taking part in the attacks, hoping to spark more fighting on the island.
Around 85 per cent of Indonesia's 220 million people follow Islam, but some areas such as Sulawesi, have roughly equal numbers of Muslims and Christians.